Mathematician Benoît Mandelbrot discussed self-similar curves, laid groundwork for fractal dimension, and examined the Coastline Paradox in a 1967 paper published in Science.

The Coastline Paradox is that the measured length of a stretch of coastline depends on the scale of measurement. Empirical evidence suggests that the smaller the increment of measurement, the longer the measured length becomes. If one were to measure a stretch of coastline with a yardstick, one would get a shorter result than if the same stretch were measured with a 30cm (one-foot) ruler. This is because one would be laying the ruler along a more curvilinear route than that followed by the yardstick.